Hi, i am struggling with the idea of basis and dim. (Headbang)

Find a basis for the subspaceSofR3spanned by

{v1 = (1,2,2),v2 = (3,2,1),v3 = (11,10,7),v4 = (7,6,4) }.

What is dims?

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- Oct 7th 2010, 05:43 PMlinalg123Find a basis for the subspace S of R3 spanned by....
Hi, i am struggling with the idea of basis and dim. (Headbang)

Find a basis for the subspace**S**of**R3**spanned by

{**v**1 = (1,2,2),**v**2 = (3,2,1),**v**3 = (11,10,7),**v**4 = (7,6,4) }.

What is dim**s****?** - Oct 8th 2010, 06:49 AMHallsofIvy
A basis is a spanning set that is also independent. You are given that this subspace is spanned by these four vectors so a basis would be a subset of that. Start with any one of them, say, v1.

v2 is not a multiple of v1 so {v1, v2} are independent.

Now look at v3. Is v3 independent of v1 and v2? That is, can v3 be written as a linear combination of v1 and v2? That is the same as asking "can we have av1+ bv2+ cv3= 0 where a, b, c are not all 0?".

If yes, add v3. If no, ask the same about v4.

Since $\displaystyle R^3$ itself has dimension 3, a basis cannot contain more than 3 vectors. - Oct 8th 2010, 04:04 PMlinalg123
ok, so i got

v3 = 2(v1) + 3(v2)

v4 = v1 + 2(v2)

so the basis is v1 and v2 and dimension 2?

Thanks for your help - Oct 9th 2010, 03:31 AMHallsofIvy
Yes, well done!